Department/Unit

Title

Abstract

We apply concepts of covariant and contravariant vector space in differential geometry and general relativity to derive new, general, exact relations between potential of mean force and free-energy profile. These relations are immensely practical in free-energy simulations because a full Jacobian transformation (which is usually unknown) is not required; rather, only knowledge of the (constraint) coordinate of interest is needed. We reveal that in addition to the Jacobian determinant, the Jacobian scale factor and Leibnizian contributions must also be considered, as well as a Fixman term with correct mass dependence. Our newly derived relations are verified with new nontrivial benchmark numerical examples for which exact results can be computed and compared with relations available in the literature that turn out to exhibit significant deviations from the exact values.

Publication Year

2012

Journal Title

Journal of Chemical Theory and Computation

Volume number

8

Issue number

11

Publisher

American Chemical Society

First Page (page number)

3998

Last Page (page number)

4003

Referreed

1

Funder

ThFinancial support provided by USNIH (GM084149 to D.M.Y.), and by the start-up fund from the HKBU Phys. Dept. and HKBU-FRG (to K.-Y.W.). Computing resources were partly provided by the HPCCC at HKBU (to K.- Y.W.).